A General Treatment of One- to Three-Dimensional Diffusion Reaction Kinetics of Interstitial Clusters: Implications for the Evolution of Voids

In recent years, it has been shown that a number of striking features in the microstructural evolution occurring in metals under cascade damage generating irradiation (e.g. enhanced swelling near grain boundaries, decoration of dislocations with SIA loops, saturation of void growth and void lattice formation) can be rationalised in terms of intra-cascade clustering of vacancies and self-interstitial atoms (SIAs), differences in the thermal stability and mobility of the resulting clusters and one-dimensional (1D) glide diffusion of SIA clusters (“production bias model”). The 1D diffusion of SIA clusters is generally disturbed by changes between equivalent 1D diffusion paths and by transversal diffusion by self-climb, resulting in diffusion reaction kinetics between the 1D and 3D limiting cases. In this paper, a general treatment of such kinetics operating in systems containing random distributions of sinks is presented. The complicated partial sink strengths of different components of the system for the annihilation of SIA clusters are expressed by those for the simple 1D and 3D limiting cases. The effects of direction changes and transversal diffusion are first considered separately and are then combined. The significance of the present treatment for damage accumulation under cascade damage conditions is illustrated by applying it to the discussion of void growth characteristics, particularly of the conditions for saturation of void growth.